# Frustrated total internal reflection: Where does energy come from?

• greypilgrim
In summary, when total internal reflection of light occurs at the boundary of an optically dense to an optically thinner medium, there is no energy flow into the thinner medium despite the electrical field not being zero. However, when an optically denser medium is added just behind the thin medium, frustrated total internal reflection occurs and a propagating wave with a nonzero Poynting vector emerges. This is possible because the evanescent field, which is "stationary" in the first case, can now penetrate the second medium and continue propagating. This phenomenon is known as the Goos-Hanchen effect and can be further explored in the provided articles.
greypilgrim
Hi,

When we have total internal reflection of light at the boundary of an optically dense to an optically thinner medium, one can show that the component of the Poynting vector perpendicular to the boundary is zero, i.e. there is no energy flow into the thinner medium. However, the electrical field is not zero in the thinner medium but decays exponentially with a certain penetration depth.

If we now add an optically denser medium just behind the thin medium, we get frustrated total internal reflection, i.e. a propagating wave in the second dense medium with a nonzero Poynting vector. How is it possible that energy crosses the thin medium although the Poynting vector in the thin medium is zero?

The evanescent field is "stationary" in the first case - hence no energy is flowing out and the Poynting vector is zero.

With the second piece of material brought close to the evanescent field it will penetrate (no longer frustrated because now it is low to high index), so it leaks through. Once it leads through into the second piece of glass the field can propagate.

You should also look into the Goos-Hanchen effect: http://en.wikipedia.org/wiki/Goos–Hänchen_effect

The following article goes into more depth:
http://www.cleyet.org/Misc._Physics/Microwave-Optics/Evanescent-FTIR/FTIR review.pdf

## What is frustrated total internal reflection?

Frustrated total internal reflection (FTIR) is a phenomenon that occurs when light traveling through a medium with a higher refractive index is partially reflected at the interface with a medium with a lower refractive index, but the remaining light is unable to escape and continues to reflect back and forth between the two interfaces.

## Where does the energy come from in frustrated total internal reflection?

The energy in frustrated total internal reflection comes from the incident light that is being partially reflected at the interface between the two mediums. This energy is then trapped and continuously reflected within the medium with the higher refractive index.

## What are the applications of frustrated total internal reflection?

FTIR has a variety of applications, including in optical communications, where it is used to create optical switches and modulators. It is also used in sensing and detection technologies, such as in biosensors and chemical sensors. Additionally, FTIR is used in microscopy and imaging techniques to create high-resolution images.

## How is frustrated total internal reflection different from total internal reflection?

Total internal reflection (TIR) occurs when light traveling through a medium with a higher refractive index is completely reflected at the interface with a medium with a lower refractive index. In contrast, FTIR occurs when the light is only partially reflected at the interface, and the remaining light is unable to escape and continues to reflect back and forth between the interfaces.

## What factors affect the intensity of frustrated total internal reflection?

The intensity of frustrated total internal reflection is affected by several factors, including the angle of incidence, the refractive indices of the two mediums, and the thickness of the medium through which the light is passing. Additionally, the polarization of the incident light and the surface roughness of the interfaces can also impact the intensity of FTIR.

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